Two teams A and B play a series of games until one team wins four games. We assume that the games are played independently and that the probability that A wins any game is p. What is the probability that the series lasts exactly five games?

Question

Mathematics

Alexis Ware

15 June, 01:04

Two teams A and B play a series of games until one team wins four games. We assume that the games are played independently and that the probability that A wins any game is p. What is the probability that the series lasts exactly five games?

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Answers (1)

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Alvaro Pierce · Answer 1

4pq (p³+q³)

Step-by-step explanation:

Exactly 5 game would be when 4 wins and 1 loss of a particular person

loss has to be one of the first 4 games

A wins: qp⁴ + pqp³ + p²qp² + p³qp

= qp⁴ + qp⁴ + qp⁴ + qp⁴ = 4qp⁴

B wins: pq⁴ + qpq³ + q²pq² + q³pq

= pq⁴ + pq⁴ + pq⁴ + pq⁴ = 4pq⁴

A wins or B wins:

4pq⁴ + 4qp⁴ = 4pq (q³+p³)